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2 years ago

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A vertical pole, 40 feet tall, casts a shadow onto the ground. If the angle of elevation from the tip of the shadow on the groun

d to the top of the pole is θ=67∘, use the dimensions given to find the length of the shadow, a, in feet. Do not include the units in your answer.

1 answer:

aksik [14]2 years ago

3 0

Answer:

Lenght of a shadow is 96.6

Step-by-step explanation:

you may use right angle triangle to find distance if you know angle of elevation.

(a) adjacent (b) hypotenuse

(c) Opposite

we know that:

adjacent (a)=40

opposite (b)=?

tan ∅= opposite/adjacent

tan 67°=opposite/40

2.4142 * 40 = adjacent

adjacent =96.6

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Solve the system of linear equations using multiplication.

Anna71 [15]

Answer:

$(8,-1)$

Step-by-step explanation:

The given system is:

$3x+3y=21$

$6x+12y=36$

Since I prefer to use smaller numbers I'm going to divide both sides of the first equation by 3 and both sides of the equation equation by 6.

This gives me the system:

$x+y=7$

$x+2y=6$

We could solve the first equation for $x$ and replace the second $x$ with that.

Let's do that.

$x+y=7$

Subtract $y$ on both sides:

$x=7-y$

So we are replacing the second $x$ in the second equation with $(7-y)$ which gives us:

$(7-y)+2y=6$

$7-y+2y=6$

$7+y=6$

$y=6-7$

$y=-1$

Now recall the first equation we arranged so that $x$ was the subject. I'm referring to $x=7-y$ .

We can now find $x$ given that $y=-1$ using the equation $x=7-y$ .

Let's do that.

$x=7-y$ with $y=-1$ :

$x=7-(-1)$

$x=7+1$

$x=8$

So the solution is (8,-1).

We can check this point by plugging it into both equations.

If both equations render true for that point, then we have verify the solution.

Let's try it.

$3x+3y=21$ with $(x,y)=(8,-1)$ :

$3(8)+3(-1)=21$

$24+(-3)=21$

$21=21$ is a true equation so the "solution" looks promising still.

$6x+12y=36$ with $(x,y)=(8,-1)$ :

$6(8)+12(-1)=36$

$48+(-12)=36$

$36=36$ is also true so the solution has been verified since both equations render true for that point.

5 0

2 years ago

Read 2 more answers

Abel is making brownies for a bake sale. The recipe shows the amount of each ingredient needed to make 9 brownies. Complete each

mixas84 [53]

Answer:

In order to make 45 brownies, Abel needs 25 cups of flour, 20 cups of sugar, 10 cups of cocoa powder and 5 eggs.

Step-by-step explanation:

As the recipe is missing in this question, the recipe is found online which given following information

Abel needs 5 cups of flour to make brownies.
If Abel uses 4 cups of sugar.
he will need to use 2 cups of cocoa powder.
The recipe will make brownies if Abel uses only 1 egg.

Abel has to make 45 brownies for the sale, this is also missing in this question, however is given in the reference question linked here.

This recipe is to make 9 brownies. Now for 45 brownies the multiplier is found as 45/9=5. So by multiplying quantity of all the ingredients by 5, Abel will be able to make 45 brownies.

Now in order to make 45 brownies

Abel needs 5*5 =25 cups of flour to make brownies.
If Abel uses 5*4=20 cups of sugar.
he will need to use 5*2=10 cups of cocoa powder.
The recipe will make brownies if Abel uses only 5*1=5 egg.

So in order to make 45 brownies, Abel needs 25 cups of flour, 20 cups of sugar, 10 cups of cocoa powder and 5 eggs.

5 0

2 years ago

Craig ran the first part of a race with an average speed of 8 miles per hour and biked the second part of a race with an average

lutik1710 [3]

Let the distance of the first part of the race be x, and that of the second part, 15 - x, then
x/8 + (15 - x)/20 = 1.125
5x + 2(15 - x) = 40 x 1.125
5x + 30 - 2x = 45
3x = 45 - 30 = 15
x = 15/3 = 5

Therefore, the distance of the first part of the race is 5 miles and the time is 5/8 = 0.625 hours or 37.5 minutes
The distance of the second part of the race is 15 - 5 = 10 miles and the time is 1.125 - 0.625 = 0.5 hours or 30 minutes.

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2 years ago

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The following exercise refers to choosing two cards from a thoroughly shuffled deck. Assume that the deck is shuffled after a ca

dem82 [27]

Answer:

$\frac{4}{663}$

Step-by-step explanation:

Given that from a well shuffled set of playing cards (52 in number) a card is drawn and without replacing it, next card is drawn.

A - the first card is 4

B - second card is ace

We have to find probability for

$A\bigcap B$

P(A) = no of 4s in the deck/total cards = $\frac{4}{52} =\frac{1}{13}$

After this first drawn if 4 is drawn, we have remaining 51 cards with 4 aces in it

P(B) = no of Aces in 51 cards/51 = $\frac{4}{51}$

Hence

$P(A\bigcap B) = \frac{1}{13} *\frac{4}{51} \\=\frac{4}{663}$

(Here we see that A and B are independent once we adjust the number of cards. Also for both we multiply the probabilities)

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2 years ago

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Tara owes $14,375 in credit card debt. The interest accrues at a rate of 5.3%. She is also borrowing $570 each month for rent fr

siniylev [52]

Answer:

$(f + g)(t) = f(t) + g(t) = 14375 (1 + \frac{5.3}{100})^{t} + 6840t$

$29619.13

Step-by-step explanation:

a. Tara has $14375 in credit card debt and the interest rate is 5.3%.

Now, if f(t) represent the amount of money Tara have in credit card debt, where t is the number of years after after interest begins to accrue, then

$f(t) = 14375 (1 + \frac{5.3}{100})^{t}$ ......... (1)

Again Tara borrows $570 each month for rent from her parents without any interest.

If g(x) represent the amount of money Tara owes to her parents, where t represents the number of years passed,then we can write

g(t) = 570 × 12t = 6840t ........ (2)

Therefore, $(f + g)(t) = f(t) + g(t) = 14375 (1 + \frac{5.3}{100})^{t} + 6840t$

b. So, for t = 2 years,

$(f + g)(t) = 14375 (1 + \frac{5.3}{100})^{2} + 6840 \times 2$ = $29619.13

So, Tara has to repay $29619.13 if she continues this way without any repayment for 2 years. (Answer)

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2 years ago