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1 year ago

In triangle △ABC, ∠ABC=90°, BH = altitude

Mathematics

1 answer:

Ainat [17]1 year ago

3 0

Answer: The exact length of segment HC is sqrt(3) units

The approximate length is roughly 1.73205080756888 (round that however you need to)

==============================================

Work Shown:

Let x = length of HC

Since AH = 3*HC, this means AH = 3*x

Draw out the picture. This step is optional but helpful in my opinion. The drawing is attached below.

After adding in the altitude BH, we have three similar triangles. So we can form the proportion shown below to solve for x

HC/BH = BH/AH

HC/3 = 3/AH ... replace BH with 3

x/3 = 3/AH ... replace HC with x

x/3 = 3/(3x) ... replace AH with 3x

x/3 = 1/x ... reduce

x*x = 3*1 ... cross multiply

x^2 = 3

x = sqrt(3) ... which is shorthand for "square root"

HC = sqrt(3)

HC = 1.73205080756888 which is approximate

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It costs 20 cents to receive a photo and 30 cents to send a photo from a cellphone. C is the cost of one photo (either sent or r

ddd [48]

Answer:

(a) PC(C)= $\left \{ {{0.6 \ \ \ \ x=20} \atop 0.4 \ \ \ \ {x=30}} \right. \\\ 0 \ \ \ \ \ \ \ else$

(b) E[C] = 24 cents

Step-by-step explanation:

Given:

Cost to receive a photo = 20 cents

Cost to send a photo = 30 cents

Probability of receiving a photo = 0.6

Probability of sending a photo = 0.4

We need to find

(a) PC(c)

(b) E[C]

Solution:

(a)

PC(C)= $\left \{ {{0.6 \ \ \ \ c=20} \atop 0.4 \ \ \ \ {c=30}} \right. \\\ 0 \ \ \ \ \ \ \ else$

(b)

Expected value can be calculated by multiplying probability with cost.

E[C] = Probability × cost

E[C] = $0.6\times20 +0.4 \times 30 = 12 + 12 = 24\ cents$

3 0

1 year ago

I talk to an average of 8 customers per hour during an 8 hour shift and need to increase the amount of customers i help by 20%,

lbvjy [14]

Answer:

The number of customer needed to achieve is 34

Step-by-step explanation:

Given as :

The number of customer per hour = 8

The time taken = 8 hours

The rate of increase = 20 %

Let The increase in number of customer after 20 % increment = x

So , The number of customer after n hours = initial number × $(1+\dfrac{\textrm rate}{100})^{n}$

or, The number of customer after 8 hours = 8 × $(1+\dfrac{\textrm 20}{100})^{8}$

or, The number of customer after 8 hours = 8 × 4.2998

∴The number of customer after 8 hours = 34.39 ≈ 34

Hence The number of customer needed to achieve is 34 answer

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2 years ago

Given: Two concentric circles with Center Point p. How many tangent lines can be drawn that both circles share?

levacccp [35]

Answer: I think that it's not One but It's ZERO because a tangent line can only touch the circle at one point and if it touches the small circle once it would have to go through the larger one twice.

Edit: I just checked and it's definitely ZERO

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1 year ago

Your drawer has 5 pairs of black socks, 4 pairs of gray socks, 2 pairs of white socks, 1 pair of brown socks, and 1 pair of blue

Sergeeva-Olga [200]

5 pairs of black socks*2 because it’s a pair= 10 socks
4 pairs of grey socks*2=8
2 pairs of white socks*2=4
1 pair of brown socks*2=2
1 pair of blue socks*2=2
10 socks+8 socks+4 socks+2 socks+ 2 socks=26 socks in total
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2 years ago

Drag and drop an answer to each box to correctly complete the explanation for deriving the formula for the volume of a sphere.

Advocard [28]

The volume of a sphere is given by:

$V= \frac{4}{3} \pi r^{3}$

So, we need to deduct this equation. We will walk through Calculus on the concept of a solid of revolution that is a solid figure that is obtained by rotating a plane curve around some straight line (the axis of revolution) that lies on the same plane. We know from calculus that:

 $V=\pi \int_{a}^{b}[f(x)]^{2}dx$

Then, according to the concept of solid of revolution we are going to rotate a circumference shown in the figure, then:

 $x^{2}+y^{2}=r^{2}$

Isolationg y:

 $y= \sqrt{r^{2}-x^{2}}$ 

So,

 $f(x)=y=\sqrt{r^{2}-x^{2}}$ 

 $V=\pi \int_{a}^{b}[\sqrt{r^{2}-x^{2}}]^{2}dx$

 $V=\pi \int_{a}^{b}(r^{2}-x^{2})dx$ 

being -r and r the limits of this integral.

 $V=\pi \int_{-r}^{r}(r^{2}-x^{2})dx$

Solving:

 $V=\pi[r^{2}x-\frac{x^{3}}{3}]\right|_{-r}^{r}$

Finally:

 $V=\pi(r^{3}-\frac{r^{3}}{3})-\pi(-r^{3}+\frac{r^{3}}{3})= \frac{4}{3} \pi r^{3}$

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2 years ago

Read 2 more answers