5. Nina has x coins. Clayton has 9 more than three times the amount that Nina has. Write a

ACD is a triangle and B is a point on AC. AB = 8cm and BC is 6cm. Angle BCD = 48° and angle BDC = 50°. (a) Find the length of BD

FromTheMoon [43]

Answer:

5.8206 cm
10.528 cm
23.056 cm^2

Step-by-step explanation:

(a) The Law of Sines can be used to find BD.

BD/sin(48°) = BD/sin(50°)

BD = (6 cm)(sin(48°)/sin(60°)) ≈ 5.82064 cm

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(b) We can use the Law of Cosines to find AD.

AD^2 = AB^2 +BD^2 -2·AB·BD·cos(98°) . . . . . angle ABD = 48°+50°

AD^2 ≈ 110.841

AD ≈ √110.841 ≈ 10.5281 . . . cm

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(c) The area of ∆ABD can be found using the formula ...

A = ab·sin(θ)/2 . . . . . where a=AB, b=BD, θ = 98°

A = (8 cm)(5.82064 cm)sin(98°)/2 ≈ 23.0560 cm^2

_____

Angle ABD is the external angle of ∆BCD that is the sum of the remote interior angles BCD and BDC. Hence ∠ABD = 48° +50° = 98°.

5 0

2 years ago

How many terms are in the algebraic expression Negative 7 + 12 x 4 minus 5 y 8 + x?

BARSIC [14]

Answer:

Therefore,

There are Four i.e 4 terms in the expression,

$-7+12x^{4}-5y^{8}+x$

Step-by-step explanation:

Algebraic Expression:

An algebraic expression is a mathematical expression that consists of variables, numbers and operations.

Variables with the coefficient is called as Term.
Number is also a term.

Here the Expression is

$-7+12x^{4}-5y^{8}+x$

So,

$-7 = One\ Term\\12x^{4}=Second\ Term\\-5y^{8}=Third\ Term\\x=Fourth\ Term$

In all there are Four i.e 4 terms in the given expressions.

Therefore,

There are Four i.e 4 terms in the expression,

$-7+12x^{4}-5y^{8}+x$

5 0

2 years ago

Read 2 more answers

Answer 0.1 is equal to or less than 5.00 plz hurry up!

Wittaler [7]

Yes, 0.1 is less than 5.00.

5.00 is a whole number, while 0.1 is less than that, so yes, you were correct.

Have a nice day! :)

7 0

1 year ago

A flat circular plate has the shape of the region x squared plus y squared less than or equals 1x2+y2≤1. the plate, including t

vredina [299]

You're looking for the extreme values of $x^2+3y^2+13x$ subject to the constraint $x^2+y^2\le1$ .

The target function has partial derivatives (set equal to 0)

$\dfrac{\partial(x^2+3y^2+13x)}{\partial x}=2x+13=0\implies x=-\dfrac{13}2$

$\dfrac{\partial(x^2+3y^2+13x)}{\partial y}=6y=0\implies y=0$

so there is only one critical point at $\left(-\dfrac{13}2,0\right)$ . But this point does not fall in the region $x^2+y^2\le1$ . There are no extreme values in the region of interest, so we check the boundary.

Parameterize the boundary of $x^2+y^2\le1$ by

$x=\cos u$

$y=\sin u$

with $0\le u$ . Then $t(x,y)$ can be considered a function of $u$ alone:

$t(x,y)=t(\cos u,\sin u)=T(u)$

$T(u)=\cos^2u+3\sin^2u+13\cos u$

$T(u)=3+13\cos u-2\cos^2u$

$T(u)$ has critical points where $T'(u)=0$ :

$T'(u)=-13\sin u+4\sin u\cos u=\sin u(4\cos u-13)=0$

$(1)\quad\sin u=0\implies u=0,u=\pi$

$(2)\quad4\cos u-13=0\implies\cos u=\dfrac{13}4$

but $|\cos u|\le1$ for all $u$ , so this case yields nothing important.

At these critical points, we have temperatures of

$T(0)=14$

$T(\pi)=-12$

so the plate is hottest at (1, 0) with a temperature of 14 (degrees?) and coldest at (-1, 0) with a temp of -12.

4 0

1 year ago

Given the formula b=rs/t solve for s

Gekata [30.6K]

Answer:

$s = \frac{bt}{r}$

Step-by-step explanation:

To solve for s, you need to follow these steps.

First multiply by t both sides of the equation.

$b = \frac{rs}{t}$

$bt = \frac{rst}{t}$

We get $bt = rs$

Now we divide by r, both sides of the equation.

$\frac{bt}{r} = \frac{rs}{r}$

Finallly we obtain:

$\frac{bt}{r} = s$ or

$s = \frac{bt}{r}$

7 0

2 years ago