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castortr0y [4]
3 years ago
9

Express in exponential form. x = logby

Mathematics
2 answers:
Lunna [17]3 years ago
6 0
X = log (base b) y
The base of the log becomes the base of the exponent.
The x and y switch.
b^x = y
shutvik [7]3 years ago
3 0

Answer:

In exponential form given equation is expressed as b^x=y

Step-by-step explanation:

Given equation is x=log_b\,y

We use the following logarithmic result,

a^{log_a\,x}=x

Consider,

x=log_b\,y

Take both to the power of b.

b^{x}=b^{log_b\,y}

b^x=y

Therefore, In exponential form given equation is expressed as b^x=y

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A model rocket is launched straight upward. The solid fuel propellant pushes the rocket off the ground at an initial velocity of
anastassius [24]

Answer:

a) 72.25sec

b) 6.25secs

c) after 10.5secs and 2 secs

Step-by-step explanation:

Given the height reached by the rocket expressed as;

s(t)= -4t^2 + 50t - 84

At maximum height, the velocity of the rocket is zero i.e ds/dt  = 0

ds/dt = -8t + 50

0 = -8t + 50

8t = 50

t = 50/8

t = 6.25secs

Hence it will reach the maximum height after 6.25secs

To get the maximum height, you will substitute t - 6.25s into the given expression

s(t)= -4t^2 + 50t - 84

s(6.25) = -4(6.25)^2 + 50(6.25) - 84

s(6.25) = -156.25 + 312.5 - 84

s(6.25)  = 72.25feet

Hence the maximum height reached by the rocket is 72.25feet

The rocket will reach the ground when s(t) = 0

Substitute into the expression

s(t)= -4t^2 + 50t - 84

0 = -4t^2 + 50t - 84

4t^2 - 50t + 84 = 0

2t^2 - 25t + 42 = 0

2t^2 - 4t - 21t + 42 = 0

2t(t-2)-21(t-2) = 0

(2t - 21) (t - 2) = 0

2t - 21 = 0 and t - 2 = 0

2t = 21 and t = 2

t = 10.5 and 2

Hence the time the rocket will reach the ground are after 10.5secs and 2 secs

3 0
3 years ago
Solve 3(2x-5)-4x+8=-1
777dan777 [17]

Answer:

6

Step-by-step explanation:

Step 1:

3 ( 2x - 5 ) - 4x + 8 = - 1

Step 2:

5x - 15 - 4x + 8 = - 1

Step 3:

x - 15 + 8 = - 1

Step 4:

x - 7 = - 1

Answer:

x = 6

Hope This Helps :)

7 0
3 years ago
Find the distance between the pair of points: (2,6) and (0,−3).
FrozenT [24]

Answer:

d = √85

Step-by-step explanation:

d^2 = (X2 - X1)^2 + (Y2 - Y1)^2

= (2 - 0)^2 + (6 + 3)^2

= 4 + 81

d = √85

3 0
2 years ago
Find an expression equivalent to 1-sinx ^2/1-cosx ^2
madam [21]

Answer:

cot²x

Step-by-step explanation:

Using the identity

sin²x + cos²x = 1, then

1 - sin²x = cos²x

1 - cos²x = sin²x

Thus

\frac{1-sin^2x}{1-cos^2x} = \frac{cos^2x}{sin^2x} = cot²x

8 0
3 years ago
A triangle is to be dilated with the origin as the center of dilation and with a scale factor of 2. Which answer choice correctl
saveliy_v [14]

Answer:

All the coordinates are changed to

(x, y) ⇒ (2x, 2y)

Step-by-step explanation:

Given - A triangle is to be dilated with the origin as the center of dilation and with a scale factor of 2.

To find -  Which answer choice correctly maps this dilation algebraically?​

Proof -

Let ABC is a triangle where A, B, C are the vertices of the triangle respectively.

Now,

Let the coordinates be (x, y)

If a triangle is to be dilated with the origin as the center of dilation and with a scale factor of a , then the coordinated be changes as

(x, y) ⇒ (ax, ay)

Here given , a = 2

So, all the coordinates are changed to

(x, y) ⇒ (2x, 2y)

3 0
2 years ago
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