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3 years ago

When Brandon went bowling, it cost $4.95 per game, plus a one-time fee to rent the shoes. Brandon played 5

Mathematics

1 answer:

vivado [14]3 years ago

8 0

7.25 the shoes I think

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I am very stuck with this

Bingel [31]

Answer:

see explanation

Step-by-step explanation:

To multiply the vector by a scalar, multiply each of the elements by the scalar.

To add 3 vectors add the corresponding elements of each vector

2a + 3b + 4c

= 2 $\left[\begin{array}{ccc}2\\3\\\end{array}\right]$ + 3 $\left[\begin{array}{ccc}-4\\1\\\end{array}\right]$ + 4 $\left[\begin{array}{ccc}3\\2\\\end{array}\right]$

= $\left[\begin{array}{ccc}4\\6\\\end{array}\right]$ + $\left[\begin{array}{ccc}-12\\3\\\end{array}\right]$ + $\left[\begin{array}{ccc}12\\8\\\end{array}\right]$

= $\left[\begin{array}{ccc}4-12+12\\6+3+8\\\end{array}\right]$

= $\left[\begin{array}{ccc}4\\17\\\end{array}\right]$

8 0

3 years ago

Find the slope of the tangent line to the given polar curve at the point specified by the value of θ

MariettaO [177]

The given curve has equation

r(θ) = 9 + 8 cos(θ)

and its derivative is

dr/dθ = -8 sin(θ)

When θ = π/3, we have r (π/3) = 13, and dr/dθ (π/3) = -4√3.

Differentiate these with respect to θ :

dy/dθ = dr/dθ sin(θ) + r(θ) cos(θ)

dx/dθ = dr/dθ cos(θ) - r(θ) sin(θ)

In polar coordinates, we have

y(θ) = r(θ) sin(θ)

x(θ) = r(θ) cos(θ)

and when θ = π/3, we have y (π/3) = 13√3/2 and x (π/3) = 13/2.

The slope of the tangent line to the curve is dy/dx. By the chain rule,

dy/dx = dy/dθ • dθ/dx = (dy/dθ) / (dx/dθ)

dy/dx = (dr/dθ sin(θ) + r(θ) cos(θ)) / (dr/dθ cos(θ) - r(θ) sin(θ))

When θ = π/3, the slope is

dy/dx = (-4√3 sin(π/3) + 13 cos(π/3)) / (-4√3 cos(π/3) - 13 sin(π/3))

dy/dx = (-4√3 (√3/2) + 13 (1/2)) / (-4√3 (1/2) - 13 (√3/2))

dy/dx = - 1/(17√3)

So, the tangent line has slope -1/(17√3) and passes through (13/2, 13√3/2). Using the point-slope formula, its equation is

y - 13√3/2 = -1/(17√3) (x - 13/2)

y = -(x - 338)/(17√3)

4 0

2 years ago

One satellite is scheduled to be launched from Cape Canaveral in Florida, and another launching is scheduled for Vandenberg Air

Lisa [10]

Answer:

$P(A) = 0.45$

$P(B) = 0.32$

Step-by-step explanation:

Given

$P(A) > P(B)$

$P(A\ u\ B) = 0.626$

$P(A\ n\ B) = 0.144$

Required

Find P(A) and P(B)

We have that:

$P(A\ u\ B) = P(A) + P(B) - P(A\ n\ B)$ --- (1)

and

$P(A\ n\ B) = P(A) * P(B)$ --- (2)

The equations become:

$P(A\ u\ B) = P(A) + P(B) - P(A\ n\ B)$ --- (1)

$0.626 = P(A) + P(B) - 0.144$

Collect like terms

$P(A) + P(B) = 0.626 + 0.144$

$P(A) + P(B) = 0.770$

Make P(A) the subject

$P(A) = 0.770 - P(B)$

$P(A\ n\ B) = P(A) * P(B)$ --- (2)

$0.144 = P(A) * P(B)$

$P(A) * P(B) = 0.144$

Substitute: $P(A) = 0.770 - P(B)$

$[0.770 - P(B)] * P(B) = 0.144$

Open bracket

$0.770P(B) - P(B)^2 = 0.144$

Represent P(B) with x

$0.770x - x^2 = 0.144$

Rewrite as:

$x^2 - 0.770x + 0.144 = 0$

Expand

$x^2 - 0.45x - 0.32x + 0.144 = 0$

Factorize:

$x[x - 0.45] - 0.32[x - 0.45]= 0$

Factor out x - 0.45

$[x - 0.32][x - 0.45]= 0$

Split

$x - 0.32= 0 \ or\ x - 0.45= 0$

Solve for x

$x = 0.32\ or\ x = 0.45$

Recall that:

$P(B) = x$

So, we have:

$P(B) = 0.32 \ or \ P(B) = 0.45$

Recall that:

$P(A) = 0.770 - P(B)$

So, we have:

$P(A) = 0.770 - 0.32 \ or\ P(A) =0.770 - 0.45$

$P(A) = 0.45 \ or\ P(A) =0.32$

Since:

$P(A) > P(B)$

Then:

$P(A) = 0.45$

$P(B) = 0.32$

6 0

3 years ago

Write the square root of 4√53/169

Anika [276]

Answer:

0.08615514661

Step-by-step explanation:

I belive this is coorect.

7 0

3 years ago

A square patio has an area of 180 square feet. How long is each side of the patio to the nearest tenth?

ikadub [295]

Answer: Squares have all 4 sides equal. Just square root 180 in a calculator and you'll get √(180)= approximately 13.4.

5 0

3 years ago